The brief arrives too late
Most copywriting briefs begin after the consequential decisions have been made. The product is fixed. The audience is presumed. The price has acquired political protection inside the organisation. Proof is whatever happens to be available. The writer is invited at the end and asked to create inevitability from contingency.
This is why apparently linguistic assignments often resist linguistic solutions. The sentence is carrying a burden produced elsewhere.
A headline is a compressed argument
The strongest headline is not an ornamental line placed above the offer. It is a compression of the market, value, mechanism, evidence and desired action. If those elements remain unstable, the headline can become clear only by becoming less true.
Before asking whether a line is persuasive, ask what conditions would make it deserved. The answer may require a narrower audience, stronger proof, a more intelligible package or a smaller promise.
The earlier practice
The copywriter who begins earlier can help the organisation distinguish a communication problem from an offer problem. This does not mean writers should seize authority over every commercial decision. It means the writing engagement must allow structural questions to be asked before verbal answers are supplied.
Sometimes the best copy decision is a product decision expressed in language. Sometimes it is the refusal to write the line the original offer appears to demand.